We present a catalog of likely astrophysical neutrino track-like events from the IceCube Neutrino Observatory. IceCube began reporting likely astrophysical neutrinos in 2016, and this system was updated in 2019. The catalog presented here includes events that were reported in real time since 2019, as well as events identified in archival data samples starting from 2011. We report 275 neutrino events from two selection channels as the first entries in the catalog, the IceCube Event Catalog of Alert Tracks, which will see ongoing extensions with additional alerts. The Gold and Bronze alert channels respectively provide neutrino candidates with a 50% and 30% probability of being astrophysical, on average assuming an astrophysical neutrino power-law energy spectral index of 2.19. For each neutrino alert, we provide the reconstructed energy, direction, false-alarm rate, probability of being astrophysical in origin, and likelihood contours describing the spatial uncertainty in the alert's reconstructed location. We also investigate a directional correlation of these neutrino events with gamma-ray and X-ray catalogs, including 4FGL, 3HWC, TeVCat, and Swift-BAT.